An adaptive double-layer structure predictive optimization control method

Abstract

This invention belongs to the field of multi-level optimization control technology, specifically relating to an adaptive two-layer predictive optimization control method. Its key feature is that it includes a steady-state target optimization layer and a dynamic control layer. The steady-state target optimization layer uses a steady-state target optimization performance function to solve for the steady-state target operating point, which is then passed to the dynamic control layer. The dynamic control layer employs an adaptive model predictive control method, designs an adaptive update rate for uncertain parameters, replaces the original parameter uncertainty model with an estimation model using the adaptive update rate, designs a model predictive control strategy to solve for the optimal control input, and passes it to the basic control layer. This invention effectively solves the uncertainty problem of the system model, ensures the closed-loop stability of the system, and effectively improves the optimal performance of the system.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-level optimization control, and in particular relates to an adaptive double-layer structure prediction optimization control method. Background Art

[0002] As science and technology drive the rapid development of industrial productivity, the scale of modern industrial production has become larger and more complex. At the same time, producers have gradually increased their requirements for productivity, not only to ensure production capacity and product quality, but also to maximize economic benefits and minimize costs. In the existing industrial production process, a hierarchical structure is adopted. The upper real-time optimization layer obtains the optimal working point through the economic optimization global production target, and then passes it to the lower dynamic control layer as the set value of this layer, optimizes and calculates the optimal operating variables, and drives the system to reach the optimal working point to achieve the goal of reducing costs and increasing efficiency. However, the existing hierarchical structure still has two shortcomings.

[0003] First, since the real-time optimization layer usually adopts a nonlinear steady-state model, while the dynamic control layer adopts a linear dynamic model, the steady-state optimal working point calculated by the real-time optimization layer is unreachable in the dynamic control layer. In addition, the execution frequency of the real-time optimization layer is slow, while the execution frequency of the dynamic control layer is fast. During an execution cycle of the real-time optimization layer, the optimal working point will migrate due to uncertain factors such as disturbances, but it will not be corrected in time, thereby reducing the optimal performance of the system.

[0004] Secondly, in the actual industrial production process, there are always some disturbances and uncertainties in the system. Most of the existing dynamic control layers directly adopt linear dynamic models and ignore these disturbances and uncertainties, which will significantly reduce the performance of the system, especially for systems with large fluctuations in the production process. It may even cause system instability. Traditional control strategies are difficult to solve disturbance and uncertainty problems. Summary of the invention

[0005] The purpose of the present invention is to provide an adaptive double-layer structure predictive optimization control method, which can effectively solve the uncertainty problem of the system model, ensure the closed-loop stability of the system, and effectively improve the optimal performance of the system.

[0006] The technical solution adopted by the present invention is as follows:

[0007] An adaptive double-layer structure predictive optimization control method is provided, which divides the original dynamic control layer into a double-layer optimization control structure, characterized in that: under the double-layer structure framework including a steady-state target optimization layer and a dynamic control layer, the steady-state target optimization layer adopts a linear steady-state gain matrix to design a steady-state target optimization performance function;

[0008] The dynamic control layer adopts an adaptive model predictive control method, and the adaptive model predictive control method also includes the following steps:

[0009] S1: Design a linear system dynamic model;

[0010] S2: Design an adaptive estimation model;

[0011] S3: Design adaptive model predictive control strategies.

[0012] In S1, the linear system dynamic model is modeled as follows:

[0013]

[0014] Among them, x a (k)∈R n ,u a (k)∈R m ,y a (k)∈R p Respectively represent the state, control input and controlled output of the system at time k; the state matrix A a ∈R n×n , input matrix B a ∈R n×m is an uncertain constant matrix, the output matrix C∈R p×n is a known constant matrix.

[0015] Convert the original system model (1) into incremental form:

[0016]

[0017] in, is the difference between the current state and the previous state; is the difference between the input at the current time and the input at the previous time; y(k) = y a (k) is the controlled output of the system; C=[0 p×n I p×p ] are the state matrix, input matrix and output matrix of the system incremental model respectively.

[0018] In S2, the estimation system model is:

[0019]

[0020] The system state and estimated system state are:

[0021]

[0022] in, According to formula (4), the system state estimation error is:

[0023]

[0024] in, On the system state estimation error The cost function is:

[0025]

[0026] Among them, the cost function About the Estimation Matrix The gradient of The gradient descent method minimizes the cost function and obtains the parameter estimation matrix as follows:

[0027]

[0028] Among them, λ>0, the estimation matrix of the system model parameters is continuously updated iteratively

[0029] According to the dynamic model of the estimated system (3), the steady-state model of the system is obtained as follows:

[0030] y ss =G ss u ss (8)

[0031] Among them, y ss 、u ss and G ss are the steady-state output, steady-state input and steady-state gain matrix after the system reaches steady state; and the soft constraint ξ is used to relax the steady-state target value y of the system. ss and the steady-state optimal value y * The relationship between.

[0032] The system steady-state target performance function is as follows:

[0033]

[0034] The system steady-state target satisfies the constraints as follows:

[0035]

[0036] Among them, Q ss and R ss is a symmetric positive definite matrix, q ss is a non-negative matrix, and y represent the upper and lower bounds of the output, respectively. and u represent the upper and lower bound constraints of the input respectively.

[0037] According to the prediction output The deviation e between the measured output y(k) is used to correct the steady-state target value by feedback:

[0038] y ss =G ss u ss +e (11)

[0039] in, Solve the steady-state target operating point (u ss ,y ss ) and passed to the dynamic control layer as the new setting value.

[0040] In S3, the adaptive model predictive control adopts terminal constraints, and the adaptive model predictive control cost function is as follows:

[0041]

[0042] Among them, the weight matrices Q1, R1 and Q2 are positive definite matrices.

[0043] The min-max optimization method is used to solve the optimization problem (12):

[0044]

[0045] Satisfy the constraints:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] Wherein, equation (14a) represents the current measurable output; equations (14b) and (14c) are the dynamic constraints of the system; equations (14d) and (14e) are the input constraints and output constraints respectively; y f ∈R p is the terminal constraint set;

[0053] The elements representing all estimated parameters belong to a set of estimated parameters.

[0054] The technical effects achieved by the present invention are:

[0055] The present invention proposes an adaptive two-layer structure predictive optimization control method, which re-divides the lower dynamic control layer of the original two-layer optimization structure into a two-layer optimization control structure, including a steady-state target optimization layer and a dynamic control layer. In the steady-state target optimization layer, a linear steady-state gain matrix is ​​used to optimize the economic benefits and the cost of variable movement within the feasible domain to obtain the steady-state target working point and pass it to the dynamic control layer; in the dynamic control layer, an adaptive model predictive control method is designed, and an estimation model with an adaptive update rate is used to replace the original parameter uncertainty model, and the optimal control input is solved and passed to the basic control layer, which effectively solves the uncertainty problem of the system model and ensures the closed-loop stability of the system. The operating frequency of the steady-state target optimization layer is the same as the execution frequency of the dynamic control layer, which effectively improves the optimal performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the double-layer optimized structure implemented in the present invention;

[0057] Figure 2 It is a flow chart of the control method implemented in the present invention;

[0058] Figure 3 It is a control block diagram for implementing the present invention;

[0059] Figure 4 It is a tracking control curve diagram of the implementation system of the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0061] like Figure 1-Figure 4 As shown in the figure, an adaptive two-layer structure predictive optimization control method is proposed. Aiming at the problem that the steady-state optimal working point calculated by the real-time optimization layer is unreachable in the dynamic control layer, the original dynamic control layer is re-divided into a two-layer optimization structure, namely, a steady-state target optimization layer and a new dynamic control layer. Under the new two-layer structure framework, the steady-state target optimization layer adopts a linear steady-state gain matrix to optimize the economic benefits and the cost of variable movement within the feasible domain to obtain the steady-state target working point closest to the steady-state optimal working point calculated by the real-time optimization layer, while the dynamic control layer adopts model predictive control (MPC) to achieve unbiased tracking of the steady-state target working point, and the operating frequency of the upper steady-state target optimization layer is the same as the execution frequency of the lower dynamic control layer, which ensures the optimality of the optimization result, thereby effectively improving the optimal performance of the system.

[0062] In addition, in response to the disturbance and uncertainty of the system, an adaptive model predictive control method is proposed in the dynamic control layer. An adaptive update law is designed to update the estimated parameters of the system online, ensuring the accuracy of the system model, and transforming the MPC problem with parameter uncertainty into an MPC problem without parameter uncertainty. The standard MPC optimization problem of the dynamic control layer is re-established, ensuring the recursive feasibility and closed-loop stability of the system;

[0063] The dynamic control layer adopts an adaptive model predictive control method, which also includes the following steps:

[0064] S1: Design a linear system dynamic model;

[0065] S2: Design an adaptive estimation model;

[0066] S3: Design adaptive model predictive control strategies.

[0067] In S1, the linear system dynamic model is as follows:

[0068]

[0069] Among them, x a (k)∈R n ,u a (k)∈R m ,y a (k)∈R p Respectively represent the state, control input and controlled output of the system at time k; the state matrix A a ∈R n×n , input matrix B a ∈R n×m is an uncertain constant matrix, the output matrix C∈R p×n is a known constant matrix. Consider converting the original system equation (1) into an incremental model:

[0070] like Figure 2 As shown, the original system model (1) is converted into incremental form:

[0071]

[0072] in, is the difference between the current state and the previous state; is the difference between the input at the current time and the input at the previous time; y(k) = y a (k) is the controlled output of the system; C=[0 p×n I p×p ] are the state matrix, input matrix and output matrix of the system incremental model respectively.

[0073] In the incremental model (2), matrices A and B are still uncertain constant matrices, and C is still a known constant matrix.

[0074]

[0075] The accuracy of the model plays an important role in MPC, and the system model matrix Θ above is uncertain, which makes subsequent prediction and optimization impossible to handle. Consider redesigning an estimation model based on the original system to improve the accuracy of the model;

[0076] The estimated system model in S2 is:

[0077]

[0078] The system state and estimated system state are:

[0079]

[0080] in, According to formula (4), the system state estimation error is:

[0081]

[0082] in, On the system state estimation error The cost function is:

[0083]

[0084] Among them, the cost function J x～ About the Estimation Matrix The gradient of The gradient descent method minimizes the cost function and obtains the parameter estimation matrix as follows:

[0085]

[0086] Among them, λ>0, the estimation matrix of the system model parameters is continuously updated iteratively

[0087] The error of the estimated parameter matrix is ​​bounded, which ensures the asymptotic stability of the state estimation error. Finally, the estimation model with adaptive rate is used to replace the original parameter uncertainty model, which ensures the stability of the system state at the equilibrium point and lays the foundation for the stability of the subsequent design of the adaptive MPC strategy.

[0088] According to formula (3), the steady-state model of the system is:

[0089] y ss =G ss uss (8)

[0090] Among them, y ss 、u ss and G ss are the steady-state output, steady-state input and steady-state gain matrix after the system reaches steady state; when the system is in an ideal state, the steady-state target operating point of the system (u ss ,y ss ) is equivalent to the system's steady-state optimal operating point (u * ,y * ), but due to the process constraints and various uncertain disturbances in the industrial system, the system cannot reach the ideal optimal working point. Therefore, consider designing a soft constraint ξ to relax the steady-state target value y ss and the steady-state optimal value y * The relationship between ξ and ξ is established. By using appropriate penalty ξ, it is ensured that relaxing the output constraint is feasible and binding. Linear penalty terms and quadratic penalty terms are added to the objective function to design precise soft constraints. When the linear penalty term is large enough, the accuracy of the soft constraint can be guaranteed. The quadratic penalty term adds an extra degree of freedom for tuning to ensure the uniqueness of the solution.

[0091] The system steady-state objective performance function is as follows:

[0092]

[0093] The system steady-state target satisfies the constraints:

[0094]

[0095] Among them, Q ss and R ss is a symmetric positive definite matrix, q ss is a non-negative matrix, and y represent the upper and lower bounds of the output, respectively. and u represent the upper and lower bounds of the input respectively; in addition, due to the interference at the output end in the steady-state target optimization layer, the introduction of the predicted output The deviation e between the measured output y(k) is used to correct the steady-state target value by feedback:

[0096] y ss =G ss u ss +e (11)

[0097] in, Solve the steady-state target operating point (u ss ,y ss ) and passed to the dynamic control layer as the new setting value.

[0098] In S3, there are various constraints in actual industrial systems. The adaptive model predictive control adopts terminal constraints. The adaptive model predictive control cost function is as follows:

[0099]

[0100] Among them, the weight matrices Q1, R1 and Q2 are positive definite. Since the model parameters are unknown, all possible situations must be considered to ensure that the constraints along the object prediction trajectory under any possible uncertainty are met, so that the performance index of the worst-case object prediction evolution is minimized. Consider designing a min-max optimization method to solve the optimization problem of the parameter uncertainty system:

[0101]

[0102] Satisfy the constraints:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Wherein, equation (14a) represents the current measurable output; equations (14b) and (14c) are the dynamic constraints of the system; equations (14d) and (14e) are the input constraints and output constraints respectively; y f ∈R p It is a terminal constraint set, which ensures that the system can be stable in the end;

[0110] The elements representing all estimated parameters belong to an estimated parameter set, and the optimal control input is solved by adaptive MPC and passed to the basic control layer.

[0111] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. An adaptive double-layer structure predictive optimization control method, characterized in that: In a two-layer structure framework including a steady-state target optimization layer and a dynamic control layer, the steady-state target optimization layer adopts a linear steady-state gain matrix to design a steady-state target optimization performance function; To solve the problem that the steady-state optimal working point calculated by the real-time optimization layer is unreachable in the dynamic control layer, the original dynamic control layer is re-divided into a two-layer optimization structure, namely a steady-state target optimization layer and a new dynamic control layer. The system steady-state target performance function is as follows: Satisfy the constraints: Among them, Q ss and R ss is a symmetric positive definite matrix, q ss is a non-negative matrix, and y Respectively represent the upper and lower bound constraints of the output, and u Respectively represent the upper and lower bound constraints of the input; The dynamic control layer adopts an adaptive model predictive control method, and the adaptive model predictive control method also includes the following steps: S1: Design a linear system dynamic model; S2: Design an adaptive estimation model; In S2, the estimated system model is: The system state and estimated system state are: in, According to formula (4), the system state estimation error is: in, On the system state estimation error The cost function is: Among them, the cost function About the Estimation Matrix The gradient of Gradient descent method minimizes the cost function Among them, λ>0, the estimated matrix of the system model parameters is continuously optimized and updated iteratively S3: Design adaptive model predictive control strategies; In S3, the adaptive model predictive control adopts terminal constraints, and the adaptive model predictive control cost function is as follows: Among them, the weight matrices Q1, R1 and Q2 are positive definite matrices.

2. The adaptive double-layer structure prediction optimization control method according to claim 1 is characterized in that: In S1, the linear system dynamic model is as follows: Among them, x a (k)∈R n ,u a (k)∈R m ,y a (k)∈R p Respectively represent the state, control input and controlled output of the system at time k; the state matrix A a ∈R n×n , input matrix B a ∈R n×m is an uncertain constant matrix, the output matrix C a ∈R p×n is a known constant matrix.

3. The adaptive double-layer structure prediction optimization control method according to claim 2 is characterized in that: Convert the original system model (1) into incremental form: Where x(k)=[Δx a (k) T y a (k) T ] T , Δx a (k) = x a (k)-x a (k-1) is the difference between the current state and the previous state; u(k) = u a (k)-u a (k-1) is the difference between the input at the current time and the input at the previous time; y(k) = y a (k) is the controlled output of the system; C=[0 p×n I p×p ] are the state matrix, input matrix and output matrix of the system incremental model respectively.

4. The adaptive double-layer structure prediction optimization control method according to claim 1, characterized in that: According to the dynamic model of the estimation system (3), the steady-state model in S3 is obtained: y ss =G ss u ss (11) Among them, y ss 、u ss and G ss are the steady-state output, steady-state input and steady-state gain matrix after the system reaches steady state; when the system is in an ideal state, the steady-state target operating point of the system (u ss ,y ss ) is equivalent to the system's steady-state optimal operating point (u * ,y * ), and use the soft constraint ξ to relax the system steady-state target value y ss and the steady-state optimal value y * The relationship between.

5. The adaptive double-layer structure prediction optimization control method according to claim 4 is characterized in that: Introducing prediction output The deviation e between the measured output y(k) is used to correct the steady-state target value by feedback: y ss =G ss u ss +e (12) in, Solve the steady-state target operating point (u ss ,y ss ) and passed to the dynamic control layer as the new setting value.

6. The adaptive double-layer structure prediction optimization control method according to claim 1, characterized in that: Use the min-max optimization method to solve the constrained optimization problem: Satisfy the constraints: Wherein, equation (14a) represents the current measurable output; equations (14b) and (14c) are the dynamic constraints of the system; equations (14d) and (14e) are the input constraints and output constraints respectively; y f ∈R p is the terminal constraint set; The elements representing all estimated parameters belong to a set of estimated parameters.

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